Getting Started

Install paste python package

You can install the package on pypi: https://pypi.org/project/paste-bio/

[1]:

import time
import pandas as pd
import numpy as np
import torch
import scanpy as sc
import matplotlib.pyplot as plt
import matplotlib.patches as mpatches
from paste3.visualization import plot_slice, stack_slices_pairwise, stack_slices_center
from paste3.paste import pairwise_align, center_align
from paste3.helper import filter_for_common_genes, match_spots_using_spatial_heuristic

Read data and create AnnData object

[2]:

data_dir = "../../../tests/data/input/"


# Assume that the coordinates of slices are named slice_name + "_coor.csv"
def load_slices(data_dir, slice_names=["slice1", "slice2", "slice3", "slice4"]):
    slices = []
    for slice_name in slice_names:
        slice_i = sc.read_csv(data_dir + slice_name + ".csv")
        slice_i_coor = np.genfromtxt(data_dir + slice_name + "_coor.csv", delimiter=",")
        slice_i.obsm["spatial"] = slice_i_coor
        # Preprocess slices
        sc.pp.filter_genes(slice_i, min_counts=15)
        sc.pp.filter_cells(slice_i, min_counts=100)
        slices.append(slice_i)
    return slices


slices = load_slices(data_dir)
slice1, slice2, slice3, slice4 = slices

Each AnnData object consists of a gene expression matrx and spatial coordinate matrix.

[3]:

slice1.X

[3]:

array([[12.,  0.,  6., ...,  0.,  0.,  0.],
       [ 7.,  0.,  1., ...,  1.,  0.,  0.],
       [15.,  1.,  4., ...,  0.,  0.,  1.],
       ...,
       [ 0.,  0.,  0., ...,  0.,  0.,  0.],
       [ 1.,  0.,  0., ...,  0.,  0.,  0.],
       [ 5.,  0.,  1., ...,  1.,  0.,  0.]], dtype=float32)

[4]:

slice1.obsm["spatial"][0:5, :]

[4]:

array([[13.064,  6.086],
       [12.116,  7.015],
       [13.945,  6.999],
       [12.987,  7.011],
       [15.011,  7.984]])

Note, you can choose to label the spots however you want. In this case, we use the default coordinates.

[5]:

slice1.obs

[5]:

	n_counts
13.064x6.086	2181.0
12.116x7.015	2295.0
13.945x6.999	3375.0
12.987x7.011	2935.0
15.011x7.984	2964.0
...	...
21.953x24.847	541.0
20.98x24.963	860.0
20.063x24.964	508.0
19.007x25.045	626.0
21.957x25.871	2515.0

254 rows × 1 columns

[6]:

slice1.var

[6]:

	n_counts
GAPDH	2233.0
UBE2G2	78.0
MAPKAPK2	255.0
NDUFA7	96.0
ASNA1	172.0
...	...
DIP2C	31.0
LYPLA2	19.0
RGP1	24.0
BPGM	17.0
HPS6	16.0

7998 rows × 1 columns

We can visualize the spatial coordinates of our slices using plot_slices.

[7]:

slice_colors = ["#e41a1c", "#377eb8", "#4daf4a", "#984ea3"]

fig, axs = plt.subplots(2, 2, figsize=(7, 7))
plot_slice(slice1, slice_colors[0], ax=axs[0, 0])
plot_slice(slice2, slice_colors[1], ax=axs[0, 1])
plot_slice(slice3, slice_colors[2], ax=axs[1, 0])
plot_slice(slice4, slice_colors[3], ax=axs[1, 1])
plt.show()

../_images/notebooks_paste_tutorial_13_0.png

We can also plot using Scanpy’s spatial plotting function.

[8]:

sc.pl.spatial(slice1, color="n_counts", spot_size=1)

../_images/notebooks_paste_tutorial_15_0.png

Pairwise Alignment

Run PASTE `pairwise_align`.

[9]:

start = time.time()

pi12 = pairwise_align(slice1, slice2)
pi23 = pairwise_align(slice2, slice3)
pi34 = pairwise_align(slice3, slice4)

print("Runtime: " + str(time.time() - start))

(INFO) (paste.py) (24-Oct-24 15:05:16) GPU is not available, resorting to torch CPU.
(INFO) (paste.py) (24-Oct-24 15:05:16) GPU is not available, resorting to torch CPU.
(INFO) (paste.py) (24-Oct-24 15:05:16) GPU is not available, resorting to torch CPU.
Runtime: 0.4124422073364258

[10]:

pd.DataFrame(pi12.cpu().numpy())

[10]:

	0	1	2	3	4	5	6	7	8	9	...	240	241	242	243	244	245	246	247	248	249
0	0.003937	0.000000	0.000000	0.0	0.0	0.000000	0.000000	0.0	0.0	0.0	...	0.0	0.000000	0.000000	0.000000	0.0	0.0	0.0	0.000000e+00	0.000000	0.000000
1	0.000063	0.003874	0.000000	0.0	0.0	0.000000	0.000000	0.0	0.0	0.0	...	0.0	0.000000	0.000000	0.000000	0.0	0.0	0.0	0.000000e+00	0.000000	0.000000
2	0.000000	0.000000	0.000000	0.0	0.0	0.003937	0.000000	0.0	0.0	0.0	...	0.0	0.000000	0.000000	0.000000	0.0	0.0	0.0	0.000000e+00	0.000000	0.000000
3	0.000000	0.000126	0.003811	0.0	0.0	0.000000	0.000000	0.0	0.0	0.0	...	0.0	0.000000	0.000000	0.000000	0.0	0.0	0.0	0.000000e+00	0.000000	0.000000
4	0.000000	0.000000	0.000000	0.0	0.0	0.000000	0.003874	0.0	0.0	0.0	...	0.0	0.000000	0.000000	0.000000	0.0	0.0	0.0	0.000000e+00	0.000000	0.000000
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
249	0.000000	0.000000	0.000000	0.0	0.0	0.000000	0.000000	0.0	0.0	0.0	...	0.0	0.000000	0.000000	0.000000	0.0	0.0	0.0	3.937008e-03	0.000000	0.000000
250	0.000000	0.000000	0.000000	0.0	0.0	0.000000	0.000000	0.0	0.0	0.0	...	0.0	0.000000	0.000000	0.000000	0.0	0.0	0.0	6.299213e-05	0.003874	0.000000
251	0.000000	0.000000	0.000000	0.0	0.0	0.000000	0.000000	0.0	0.0	0.0	...	0.0	0.000000	0.000126	0.003811	0.0	0.0	0.0	3.035766e-17	0.000000	0.000000
252	0.000000	0.000000	0.000000	0.0	0.0	0.000000	0.000000	0.0	0.0	0.0	...	0.0	0.003748	0.000000	0.000189	0.0	0.0	0.0	0.000000e+00	0.000000	0.000000
253	0.000000	0.000000	0.000000	0.0	0.0	0.000000	0.000000	0.0	0.0	0.0	...	0.0	0.000000	0.000000	0.000000	0.0	0.0	0.0	0.000000e+00	0.000000	0.003937

254 rows × 250 columns

Sequential pairwise slice alignment plots

[11]:

pis = [pi12, pi23, pi34]
slices = [slice1, slice2, slice3, slice4]

new_slices = stack_slices_pairwise(slices, pis)

Now that we’ve aligned the spatial coordinates, we can plot them all on the same coordinate system.

[12]:

slice_colors = ["#e41a1c", "#377eb8", "#4daf4a", "#984ea3"]

plt.figure(figsize=(7, 7))
for i in range(len(new_slices)):
    plot_slice(new_slices[i], slice_colors[i], s=400)
plt.legend(
    handles=[
        mpatches.Patch(color=slice_colors[0], label="1"),
        mpatches.Patch(color=slice_colors[1], label="2"),
        mpatches.Patch(color=slice_colors[2], label="3"),
        mpatches.Patch(color=slice_colors[3], label="4"),
    ]
)
plt.gca().invert_yaxis()
plt.axis("off")
plt.show()

../_images/notebooks_paste_tutorial_23_0.png

We can also plot pairwise layers together.

[13]:

slice_colors = ["#e41a1c", "#377eb8", "#4daf4a", "#984ea3"]

fig, axs = plt.subplots(2, 2, figsize=(7, 7))
plot_slice(new_slices[0], slice_colors[0], ax=axs[0, 0])
plot_slice(new_slices[1], slice_colors[1], ax=axs[0, 0])
plot_slice(new_slices[1], slice_colors[1], ax=axs[0, 1])
plot_slice(new_slices[2], slice_colors[2], ax=axs[0, 1])
plot_slice(new_slices[2], slice_colors[2], ax=axs[1, 0])
plot_slice(new_slices[3], slice_colors[3], ax=axs[1, 0])
fig.delaxes(axs[1, 1])
plt.show()

../_images/notebooks_paste_tutorial_25_0.png

We can also plot the slices in 3-D.

[14]:

import plotly.express as px
import plotly.io as pio

pio.renderers.default = "notebook"

slices_colors = ["#e41a1c", "#377eb8", "#4daf4a", "#984ea3"]

# scale the distance between layers
z_scale = 2

values = []
for i, L in enumerate(new_slices):
    for x, y in L.obsm["spatial"]:
        values.append([x, y, i * z_scale, str(i)])
df = pd.DataFrame(values, columns=["x", "y", "z", "slice"])
fig = px.scatter_3d(
    df, x="x", y="y", z="z", color="slice", color_discrete_sequence=slice_colors
)
fig.update_layout(scene_aspectmode="data")
fig.show()

Center Alignment

First, we will read in and preprocess the data (if you ran pairwise_align above, it will be altered).

[15]:

slices = load_slices(data_dir)
slice1, slice2, slice3, slice4 = slices

Run PASTE `center_align`.

[16]:

slices = [slice1, slice2, slice3, slice4]
initial_slice = slice1.copy()
lmbda = len(slices) * [1 / len(slices)]

Now, for center alignment, we can provide initial mappings between the center and original slices to PASTE to improve the algorithm. However, note this is optional.

[17]:

filter_for_common_genes(slices)

b = []
for i in range(len(slices)):
    b.append(
        torch.Tensor(
            match_spots_using_spatial_heuristic(slices[0].X, slices[i].X)
        ).double()
    )

(INFO) (helper.py) (24-Oct-24 15:05:18) Filtered all slices for common genes. There are 6397 common genes.

[18]:

start = time.time()

center_slice, pis = center_align(
    initial_slice, slices, lmbda, random_seed=5, pis_init=b
)

print("Runtime: " + str(time.time() - start))

(INFO) (paste.py) (24-Oct-24 15:05:28) GPU is not available, resorting to torch CPU.
(INFO) (paste.py) (24-Oct-24 15:05:28) Filtered all slices for common genes. There are 6397 common genes.
(INFO) (paste.py) (24-Oct-24 15:05:30) Iteration: 0
(INFO) (paste.py) (24-Oct-24 15:05:30) Solving Pairwise Slice Alignment Problem.

/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/sklearn/decomposition/_nmf.py:1759: ConvergenceWarning:

Maximum number of iterations 200 reached. Increase it to improve convergence.

(INFO) (paste.py) (24-Oct-24 15:05:31) Solving Center Mapping NMF Problem.

/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/sklearn/decomposition/_nmf.py:1759: ConvergenceWarning:

Maximum number of iterations 200 reached. Increase it to improve convergence.

--- Logging error ---

(INFO) (paste.py) (24-Oct-24 15:05:34) Difference: 13.865903709734415

(INFO) (paste.py) (24-Oct-24 15:05:34) Iteration: 1
(INFO) (paste.py) (24-Oct-24 15:05:34) Solving Pairwise Slice Alignment Problem.

Traceback (most recent call last):
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/logging/__init__.py", line 1160, in emit
    msg = self.format(record)
          ^^^^^^^^^^^^^^^^^^^
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/logging/__init__.py", line 999, in format
    return fmt.format(record)
           ^^^^^^^^^^^^^^^^^^
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/logging/__init__.py", line 703, in format
    record.message = record.getMessage()
                     ^^^^^^^^^^^^^^^^^^^
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/logging/__init__.py", line 392, in getMessage
    msg = msg % self.args
          ~~~~^~~~~~~~~~~
TypeError: not all arguments converted during string formatting
Call stack:
  File "<frozen runpy>", line 198, in _run_module_as_main
  File "<frozen runpy>", line 88, in _run_code
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/ipykernel_launcher.py", line 18, in <module>
    app.launch_new_instance()
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/traitlets/config/application.py", line 1075, in launch_instance
    app.start()
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/ipykernel/kernelapp.py", line 739, in start
    self.io_loop.start()
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/tornado/platform/asyncio.py", line 205, in start
    self.asyncio_loop.run_forever()
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/asyncio/base_events.py", line 641, in run_forever
    self._run_once()
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/asyncio/base_events.py", line 1986, in _run_once
    handle._run()
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/asyncio/events.py", line 88, in _run
    self._context.run(self._callback, *self._args)
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/ipykernel/kernelbase.py", line 545, in dispatch_queue
    await self.process_one()
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/ipykernel/kernelbase.py", line 534, in process_one
    await dispatch(*args)
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/ipykernel/kernelbase.py", line 437, in dispatch_shell
    await result
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/ipykernel/ipkernel.py", line 362, in execute_request
    await super().execute_request(stream, ident, parent)
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/ipykernel/kernelbase.py", line 778, in execute_request
    reply_content = await reply_content
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/ipykernel/ipkernel.py", line 449, in do_execute
    res = shell.run_cell(
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/ipykernel/zmqshell.py", line 549, in run_cell
    return super().run_cell(*args, **kwargs)
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/IPython/core/interactiveshell.py", line 3075, in run_cell
    result = self._run_cell(
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/IPython/core/interactiveshell.py", line 3130, in _run_cell
    result = runner(coro)
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/IPython/core/async_helpers.py", line 128, in _pseudo_sync_runner
    coro.send(None)
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/IPython/core/interactiveshell.py", line 3334, in run_cell_async
    has_raised = await self.run_ast_nodes(code_ast.body, cell_name,
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/IPython/core/interactiveshell.py", line 3517, in run_ast_nodes
    if await self.run_code(code, result, async_=asy):
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/IPython/core/interactiveshell.py", line 3577, in run_code
    exec(code_obj, self.user_global_ns, self.user_ns)
  File "/tmp/ipykernel_2356/1787050896.py", line 3, in <module>
    center_slice, pis = center_align(
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/paste3/paste.py", line 335, in center_align
    logger.info("Objective ", R_new)
Message: 'Objective '
Arguments: (-13.865903709734415,)

(INFO) (paste.py) (24-Oct-24 15:05:34) Solving Center Mapping NMF Problem.
(INFO) (paste.py) (24-Oct-24 15:05:37) Difference: 15.248865904870266

(INFO) (paste.py) (24-Oct-24 15:05:37) Iteration: 2
(INFO) (paste.py) (24-Oct-24 15:05:37) Solving Pairwise Slice Alignment Problem.

/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/sklearn/decomposition/_nmf.py:1759: ConvergenceWarning:

Maximum number of iterations 200 reached. Increase it to improve convergence.

--- Logging error ---
Traceback (most recent call last):
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/logging/__init__.py", line 1160, in emit
    msg = self.format(record)
          ^^^^^^^^^^^^^^^^^^^
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/logging/__init__.py", line 999, in format
    return fmt.format(record)
           ^^^^^^^^^^^^^^^^^^
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/logging/__init__.py", line 703, in format
    record.message = record.getMessage()
                     ^^^^^^^^^^^^^^^^^^^
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/logging/__init__.py", line 392, in getMessage
    msg = msg % self.args
          ~~~~^~~~~~~~~~~
TypeError: not all arguments converted during string formatting
Call stack:
  File "<frozen runpy>", line 198, in _run_module_as_main
  File "<frozen runpy>", line 88, in _run_code
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/ipykernel_launcher.py", line 18, in <module>
    app.launch_new_instance()
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/traitlets/config/application.py", line 1075, in launch_instance
    app.start()
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/ipykernel/kernelapp.py", line 739, in start
    self.io_loop.start()
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/tornado/platform/asyncio.py", line 205, in start
    self.asyncio_loop.run_forever()
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/asyncio/base_events.py", line 641, in run_forever
    self._run_once()
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/asyncio/base_events.py", line 1986, in _run_once
    handle._run()
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/asyncio/events.py", line 88, in _run
    self._context.run(self._callback, *self._args)
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/ipykernel/kernelbase.py", line 545, in dispatch_queue
    await self.process_one()
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/ipykernel/kernelbase.py", line 534, in process_one
    await dispatch(*args)
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/ipykernel/kernelbase.py", line 437, in dispatch_shell
    await result
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/ipykernel/ipkernel.py", line 362, in execute_request
    await super().execute_request(stream, ident, parent)
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/ipykernel/kernelbase.py", line 778, in execute_request
    reply_content = await reply_content
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/ipykernel/ipkernel.py", line 449, in do_execute
    res = shell.run_cell(
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/ipykernel/zmqshell.py", line 549, in run_cell
    return super().run_cell(*args, **kwargs)
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/IPython/core/interactiveshell.py", line 3075, in run_cell
    result = self._run_cell(
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/IPython/core/interactiveshell.py", line 3130, in _run_cell
    result = runner(coro)
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/IPython/core/async_helpers.py", line 128, in _pseudo_sync_runner
    coro.send(None)
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/IPython/core/interactiveshell.py", line 3334, in run_cell_async
    has_raised = await self.run_ast_nodes(code_ast.body, cell_name,
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/IPython/core/interactiveshell.py", line 3517, in run_ast_nodes
    if await self.run_code(code, result, async_=asy):
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/IPython/core/interactiveshell.py", line 3577, in run_code
    exec(code_obj, self.user_global_ns, self.user_ns)
  File "/tmp/ipykernel_2356/1787050896.py", line 3, in <module>
    center_slice, pis = center_align(
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/paste3/paste.py", line 335, in center_align
    logger.info("Objective ", R_new)
Message: 'Objective '
Arguments: (1.3829621951358517,)

(INFO) (paste.py) (24-Oct-24 15:05:37) Solving Center Mapping NMF Problem.
(INFO) (paste.py) (24-Oct-24 15:05:40) Difference: 0.005131013408118834

(INFO) (paste.py) (24-Oct-24 15:05:40) Iteration: 3
(INFO) (paste.py) (24-Oct-24 15:05:40) Solving Pairwise Slice Alignment Problem.

/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/sklearn/decomposition/_nmf.py:1759: ConvergenceWarning:

Maximum number of iterations 200 reached. Increase it to improve convergence.

--- Logging error ---
Traceback (most recent call last):
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/logging/__init__.py", line 1160, in emit
    msg = self.format(record)
          ^^^^^^^^^^^^^^^^^^^
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/logging/__init__.py", line 999, in format
    return fmt.format(record)
           ^^^^^^^^^^^^^^^^^^
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/logging/__init__.py", line 703, in format
    record.message = record.getMessage()
                     ^^^^^^^^^^^^^^^^^^^
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/logging/__init__.py", line 392, in getMessage
    msg = msg % self.args
          ~~~~^~~~~~~~~~~
TypeError: not all arguments converted during string formatting
Call stack:
  File "<frozen runpy>", line 198, in _run_module_as_main
  File "<frozen runpy>", line 88, in _run_code
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/ipykernel_launcher.py", line 18, in <module>
    app.launch_new_instance()
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/traitlets/config/application.py", line 1075, in launch_instance
    app.start()
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/ipykernel/kernelapp.py", line 739, in start
    self.io_loop.start()
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/tornado/platform/asyncio.py", line 205, in start
    self.asyncio_loop.run_forever()
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/asyncio/base_events.py", line 641, in run_forever
    self._run_once()
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/asyncio/base_events.py", line 1986, in _run_once
    handle._run()
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/asyncio/events.py", line 88, in _run
    self._context.run(self._callback, *self._args)
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/ipykernel/kernelbase.py", line 545, in dispatch_queue
    await self.process_one()
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/ipykernel/kernelbase.py", line 534, in process_one
    await dispatch(*args)
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/ipykernel/kernelbase.py", line 437, in dispatch_shell
    await result
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/ipykernel/ipkernel.py", line 362, in execute_request
    await super().execute_request(stream, ident, parent)
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/ipykernel/kernelbase.py", line 778, in execute_request
    reply_content = await reply_content
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/ipykernel/ipkernel.py", line 449, in do_execute
    res = shell.run_cell(
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/ipykernel/zmqshell.py", line 549, in run_cell
    return super().run_cell(*args, **kwargs)
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/IPython/core/interactiveshell.py", line 3075, in run_cell
    result = self._run_cell(
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/IPython/core/interactiveshell.py", line 3130, in _run_cell
    result = runner(coro)
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/IPython/core/async_helpers.py", line 128, in _pseudo_sync_runner
    coro.send(None)
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/IPython/core/interactiveshell.py", line 3334, in run_cell_async
    has_raised = await self.run_ast_nodes(code_ast.body, cell_name,
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/IPython/core/interactiveshell.py", line 3517, in run_ast_nodes
    if await self.run_code(code, result, async_=asy):
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/IPython/core/interactiveshell.py", line 3577, in run_code
    exec(code_obj, self.user_global_ns, self.user_ns)
  File "/tmp/ipykernel_2356/1787050896.py", line 3, in <module>
    center_slice, pis = center_align(
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/paste3/paste.py", line 335, in center_align
    logger.info("Objective ", R_new)
Message: 'Objective '
Arguments: (1.3880932085439706,)

(INFO) (paste.py) (24-Oct-24 15:05:40) Solving Center Mapping NMF Problem.
(INFO) (paste.py) (24-Oct-24 15:05:43) Difference: 0.003430002043694369

(INFO) (paste.py) (24-Oct-24 15:05:43) Iteration: 4
(INFO) (paste.py) (24-Oct-24 15:05:43) Solving Pairwise Slice Alignment Problem.

/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/sklearn/decomposition/_nmf.py:1759: ConvergenceWarning:

Maximum number of iterations 200 reached. Increase it to improve convergence.

--- Logging error ---
Traceback (most recent call last):
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/logging/__init__.py", line 1160, in emit
    msg = self.format(record)
          ^^^^^^^^^^^^^^^^^^^
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/logging/__init__.py", line 999, in format
    return fmt.format(record)
           ^^^^^^^^^^^^^^^^^^
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/logging/__init__.py", line 703, in format
    record.message = record.getMessage()
                     ^^^^^^^^^^^^^^^^^^^
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/logging/__init__.py", line 392, in getMessage
    msg = msg % self.args
          ~~~~^~~~~~~~~~~
TypeError: not all arguments converted during string formatting
Call stack:
  File "<frozen runpy>", line 198, in _run_module_as_main
  File "<frozen runpy>", line 88, in _run_code
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/ipykernel_launcher.py", line 18, in <module>
    app.launch_new_instance()
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/traitlets/config/application.py", line 1075, in launch_instance
    app.start()
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/ipykernel/kernelapp.py", line 739, in start
    self.io_loop.start()
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/tornado/platform/asyncio.py", line 205, in start
    self.asyncio_loop.run_forever()
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/asyncio/base_events.py", line 641, in run_forever
    self._run_once()
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/asyncio/base_events.py", line 1986, in _run_once
    handle._run()
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/asyncio/events.py", line 88, in _run
    self._context.run(self._callback, *self._args)
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/ipykernel/kernelbase.py", line 545, in dispatch_queue
    await self.process_one()
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/ipykernel/kernelbase.py", line 534, in process_one
    await dispatch(*args)
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/ipykernel/kernelbase.py", line 437, in dispatch_shell
    await result
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/ipykernel/ipkernel.py", line 362, in execute_request
    await super().execute_request(stream, ident, parent)
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/ipykernel/kernelbase.py", line 778, in execute_request
    reply_content = await reply_content
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/ipykernel/ipkernel.py", line 449, in do_execute
    res = shell.run_cell(
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/ipykernel/zmqshell.py", line 549, in run_cell
    return super().run_cell(*args, **kwargs)
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/IPython/core/interactiveshell.py", line 3075, in run_cell
    result = self._run_cell(
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/IPython/core/interactiveshell.py", line 3130, in _run_cell
    result = runner(coro)
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/IPython/core/async_helpers.py", line 128, in _pseudo_sync_runner
    coro.send(None)
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/IPython/core/interactiveshell.py", line 3334, in run_cell_async
    has_raised = await self.run_ast_nodes(code_ast.body, cell_name,
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/IPython/core/interactiveshell.py", line 3517, in run_ast_nodes
    if await self.run_code(code, result, async_=asy):
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/IPython/core/interactiveshell.py", line 3577, in run_code
    exec(code_obj, self.user_global_ns, self.user_ns)
  File "/tmp/ipykernel_2356/1787050896.py", line 3, in <module>
    center_slice, pis = center_align(
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/paste3/paste.py", line 335, in center_align
    logger.info("Objective ", R_new)
Message: 'Objective '
Arguments: (1.391523210587665,)

(INFO) (paste.py) (24-Oct-24 15:05:43) Solving Center Mapping NMF Problem.
(INFO) (paste.py) (24-Oct-24 15:05:46) Difference: 0.0015480271150865033

(INFO) (paste.py) (24-Oct-24 15:05:46) Iteration: 5
(INFO) (paste.py) (24-Oct-24 15:05:46) Solving Pairwise Slice Alignment Problem.

/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/sklearn/decomposition/_nmf.py:1759: ConvergenceWarning:

Maximum number of iterations 200 reached. Increase it to improve convergence.

--- Logging error ---
Traceback (most recent call last):
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/logging/__init__.py", line 1160, in emit
    msg = self.format(record)
          ^^^^^^^^^^^^^^^^^^^
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/logging/__init__.py", line 999, in format
    return fmt.format(record)
           ^^^^^^^^^^^^^^^^^^
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/logging/__init__.py", line 703, in format
    record.message = record.getMessage()
                     ^^^^^^^^^^^^^^^^^^^
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/logging/__init__.py", line 392, in getMessage
    msg = msg % self.args
          ~~~~^~~~~~~~~~~
TypeError: not all arguments converted during string formatting
Call stack:
  File "<frozen runpy>", line 198, in _run_module_as_main
  File "<frozen runpy>", line 88, in _run_code
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/ipykernel_launcher.py", line 18, in <module>
    app.launch_new_instance()
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/traitlets/config/application.py", line 1075, in launch_instance
    app.start()
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/ipykernel/kernelapp.py", line 739, in start
    self.io_loop.start()
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/tornado/platform/asyncio.py", line 205, in start
    self.asyncio_loop.run_forever()
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/asyncio/base_events.py", line 641, in run_forever
    self._run_once()
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/asyncio/base_events.py", line 1986, in _run_once
    handle._run()
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/asyncio/events.py", line 88, in _run
    self._context.run(self._callback, *self._args)
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/ipykernel/kernelbase.py", line 545, in dispatch_queue
    await self.process_one()
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/ipykernel/kernelbase.py", line 534, in process_one
    await dispatch(*args)
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/ipykernel/kernelbase.py", line 437, in dispatch_shell
    await result
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/ipykernel/ipkernel.py", line 362, in execute_request
    await super().execute_request(stream, ident, parent)
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/ipykernel/kernelbase.py", line 778, in execute_request
    reply_content = await reply_content
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/ipykernel/ipkernel.py", line 449, in do_execute
    res = shell.run_cell(
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/ipykernel/zmqshell.py", line 549, in run_cell
    return super().run_cell(*args, **kwargs)
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/IPython/core/interactiveshell.py", line 3075, in run_cell
    result = self._run_cell(
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/IPython/core/interactiveshell.py", line 3130, in _run_cell
    result = runner(coro)
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/IPython/core/async_helpers.py", line 128, in _pseudo_sync_runner
    coro.send(None)
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/IPython/core/interactiveshell.py", line 3334, in run_cell_async
    has_raised = await self.run_ast_nodes(code_ast.body, cell_name,
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/IPython/core/interactiveshell.py", line 3517, in run_ast_nodes
    if await self.run_code(code, result, async_=asy):
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/IPython/core/interactiveshell.py", line 3577, in run_code
    exec(code_obj, self.user_global_ns, self.user_ns)
  File "/tmp/ipykernel_2356/1787050896.py", line 3, in <module>
    center_slice, pis = center_align(
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/paste3/paste.py", line 335, in center_align
    logger.info("Objective ", R_new)
Message: 'Objective '
Arguments: (1.3930712377027514,)

(INFO) (paste.py) (24-Oct-24 15:05:46) Solving Center Mapping NMF Problem.
(INFO) (paste.py) (24-Oct-24 15:05:49) Difference: 0.0021792482998677087

(INFO) (paste.py) (24-Oct-24 15:05:49) Iteration: 6
(INFO) (paste.py) (24-Oct-24 15:05:49) Solving Pairwise Slice Alignment Problem.

/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/sklearn/decomposition/_nmf.py:1759: ConvergenceWarning:

Maximum number of iterations 200 reached. Increase it to improve convergence.

--- Logging error ---
Traceback (most recent call last):
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/logging/__init__.py", line 1160, in emit
    msg = self.format(record)
          ^^^^^^^^^^^^^^^^^^^
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/logging/__init__.py", line 999, in format
    return fmt.format(record)
           ^^^^^^^^^^^^^^^^^^
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/logging/__init__.py", line 703, in format
    record.message = record.getMessage()
                     ^^^^^^^^^^^^^^^^^^^
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/logging/__init__.py", line 392, in getMessage
    msg = msg % self.args
          ~~~~^~~~~~~~~~~
TypeError: not all arguments converted during string formatting
Call stack:
  File "<frozen runpy>", line 198, in _run_module_as_main
  File "<frozen runpy>", line 88, in _run_code
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/ipykernel_launcher.py", line 18, in <module>
    app.launch_new_instance()
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/traitlets/config/application.py", line 1075, in launch_instance
    app.start()
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/ipykernel/kernelapp.py", line 739, in start
    self.io_loop.start()
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/tornado/platform/asyncio.py", line 205, in start
    self.asyncio_loop.run_forever()
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/asyncio/base_events.py", line 641, in run_forever
    self._run_once()
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/asyncio/base_events.py", line 1986, in _run_once
    handle._run()
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/asyncio/events.py", line 88, in _run
    self._context.run(self._callback, *self._args)
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/ipykernel/kernelbase.py", line 545, in dispatch_queue
    await self.process_one()
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/ipykernel/kernelbase.py", line 534, in process_one
    await dispatch(*args)
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/ipykernel/kernelbase.py", line 437, in dispatch_shell
    await result
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/ipykernel/ipkernel.py", line 362, in execute_request
    await super().execute_request(stream, ident, parent)
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/ipykernel/kernelbase.py", line 778, in execute_request
    reply_content = await reply_content
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/ipykernel/ipkernel.py", line 449, in do_execute
    res = shell.run_cell(
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/ipykernel/zmqshell.py", line 549, in run_cell
    return super().run_cell(*args, **kwargs)
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/IPython/core/interactiveshell.py", line 3075, in run_cell
    result = self._run_cell(
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/IPython/core/interactiveshell.py", line 3130, in _run_cell
    result = runner(coro)
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/IPython/core/async_helpers.py", line 128, in _pseudo_sync_runner
    coro.send(None)
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/IPython/core/interactiveshell.py", line 3334, in run_cell_async
    has_raised = await self.run_ast_nodes(code_ast.body, cell_name,
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/IPython/core/interactiveshell.py", line 3517, in run_ast_nodes
    if await self.run_code(code, result, async_=asy):
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/IPython/core/interactiveshell.py", line 3577, in run_code
    exec(code_obj, self.user_global_ns, self.user_ns)
  File "/tmp/ipykernel_2356/1787050896.py", line 3, in <module>
    center_slice, pis = center_align(
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/paste3/paste.py", line 335, in center_align
    logger.info("Objective ", R_new)
Message: 'Objective '
Arguments: (1.3952504860026191,)

(INFO) (paste.py) (24-Oct-24 15:05:49) Solving Center Mapping NMF Problem.
(INFO) (paste.py) (24-Oct-24 15:05:52) Difference: 0.00012856863721055767

Runtime: 24.505126237869263

/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/sklearn/decomposition/_nmf.py:1759: ConvergenceWarning:

Maximum number of iterations 200 reached. Increase it to improve convergence.

--- Logging error ---
Traceback (most recent call last):
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/logging/__init__.py", line 1160, in emit
    msg = self.format(record)
          ^^^^^^^^^^^^^^^^^^^
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/logging/__init__.py", line 999, in format
    return fmt.format(record)
           ^^^^^^^^^^^^^^^^^^
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/logging/__init__.py", line 703, in format
    record.message = record.getMessage()
                     ^^^^^^^^^^^^^^^^^^^
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/logging/__init__.py", line 392, in getMessage
    msg = msg % self.args
          ~~~~^~~~~~~~~~~
TypeError: not all arguments converted during string formatting
Call stack:
  File "<frozen runpy>", line 198, in _run_module_as_main
  File "<frozen runpy>", line 88, in _run_code
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/ipykernel_launcher.py", line 18, in <module>
    app.launch_new_instance()
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/traitlets/config/application.py", line 1075, in launch_instance
    app.start()
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/ipykernel/kernelapp.py", line 739, in start
    self.io_loop.start()
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/tornado/platform/asyncio.py", line 205, in start
    self.asyncio_loop.run_forever()
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/asyncio/base_events.py", line 641, in run_forever
    self._run_once()
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/asyncio/base_events.py", line 1986, in _run_once
    handle._run()
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/asyncio/events.py", line 88, in _run
    self._context.run(self._callback, *self._args)
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/ipykernel/kernelbase.py", line 545, in dispatch_queue
    await self.process_one()
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/ipykernel/kernelbase.py", line 534, in process_one
    await dispatch(*args)
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/ipykernel/kernelbase.py", line 437, in dispatch_shell
    await result
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/ipykernel/ipkernel.py", line 362, in execute_request
    await super().execute_request(stream, ident, parent)
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/ipykernel/kernelbase.py", line 778, in execute_request
    reply_content = await reply_content
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/ipykernel/ipkernel.py", line 449, in do_execute
    res = shell.run_cell(
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/ipykernel/zmqshell.py", line 549, in run_cell
    return super().run_cell(*args, **kwargs)
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/IPython/core/interactiveshell.py", line 3075, in run_cell
    result = self._run_cell(
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/IPython/core/interactiveshell.py", line 3130, in _run_cell
    result = runner(coro)
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/IPython/core/async_helpers.py", line 128, in _pseudo_sync_runner
    coro.send(None)
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/IPython/core/interactiveshell.py", line 3334, in run_cell_async
    has_raised = await self.run_ast_nodes(code_ast.body, cell_name,
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/IPython/core/interactiveshell.py", line 3517, in run_ast_nodes
    if await self.run_code(code, result, async_=asy):
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/IPython/core/interactiveshell.py", line 3577, in run_code
    exec(code_obj, self.user_global_ns, self.user_ns)
  File "/tmp/ipykernel_2356/1787050896.py", line 3, in <module>
    center_slice, pis = center_align(
  File "/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/paste3/paste.py", line 335, in center_align
    logger.info("Objective ", R_new)
Message: 'Objective '
Arguments: (1.3953790546398297,)

Again, we can run center align without providing intial mappings below.

[19]:

# center_slice, pis = paste.center_align(initial_slice, slices, lmbda, random_seed = 5)

center_slice returns an AnnData object that also includes the low dimensional representation of our inferred center slice.

[20]:

center_slice.uns["paste_W"]

[20]:

array([[2.56406093e-02, 1.17735607e+00, 1.45992052e-01, ...,
        1.67005417e-02, 8.65816825e-03, 1.64249357e-02],
       [1.93239958e-03, 3.38372964e-01, 1.80787142e-01, ...,
        1.61882816e-02, 1.01921082e-03, 4.46527741e-02],
       [4.19665776e-01, 1.88694807e-01, 2.90303299e-02, ...,
        4.75023417e-02, 1.62389942e-02, 1.17923347e-01],
       ...,
       [2.91596137e-02, 8.19205067e-03, 1.07181457e-01, ...,
        4.61294221e-04, 4.20524970e-04, 2.33305743e-01],
       [4.31159614e-02, 3.82986845e-02, 1.78688011e-01, ...,
        9.82425940e-03, 3.23265908e-03, 2.58807000e-01],
       [1.83314287e-01, 1.68948944e-05, 2.22536847e-02, ...,
        1.16837125e-05, 4.58040722e-03, 9.97049974e-02]])

[21]:

center_slice.uns["paste_H"]

[21]:

array([[9.00595607e-01, 1.28095198e-01, 7.99820095e-02, ...,
        5.45671921e-03, 4.42535702e-02, 2.77099831e-02],
       [1.84556879e+00, 1.12907519e-01, 3.19053467e-01, ...,
        1.01912359e-01, 1.03440812e-01, 3.08299141e-02],
       [1.93982112e+00, 1.42403635e-01, 1.30713055e-01, ...,
        7.35120043e-02, 3.50568629e-02, 2.86018512e-02],
       ...,
       [3.05294214e+00, 1.88580787e-01, 3.20976584e-01, ...,
        2.51081654e-02, 5.00735520e-06, 1.10129733e-02],
       [9.20159439e-01, 1.65184158e-01, 1.04867309e-01, ...,
        1.26153756e-02, 1.25054025e-02, 2.44712738e-02],
       [5.73756511e+00, 7.43537991e-04, 3.13147992e-01, ...,
        6.80617618e-06, 3.99149859e-02, 2.55630212e-13]])

Center slice alignment plots

Next, we can use the outputs of center_align to align the slices.

[22]:

center, new_slices = stack_slices_center(center_slice, slices, pis)

Now that we’ve aligned the spatial coordinates, we can plot them all on the same coordinate system. Note the center slice is not plotted.

[23]:

center_color = "orange"
slices_colors = ["#e41a1c", "#377eb8", "#4daf4a", "#984ea3"]

plt.figure(figsize=(7, 7))
plot_slice(center, center_color, s=400)
for i in range(len(new_slices)):
    plot_slice(new_slices[i], slices_colors[i], s=400)

plt.legend(
    handles=[
        mpatches.Patch(color=slices_colors[0], label="1"),
        mpatches.Patch(color=slices_colors[1], label="2"),
        mpatches.Patch(color=slices_colors[2], label="3"),
        mpatches.Patch(color=slices_colors[3], label="4"),
    ]
)
plt.gca().invert_yaxis()
plt.axis("off")
plt.show()

../_images/notebooks_paste_tutorial_45_0.png

Next, we plot each slice compared to the center.

Note that since we used slice1 as the coordinates for the center slice, they remain the same, and thus we cannot see both in our plots below.

[24]:

center_color = "orange"
slice_colors = ["#e41a1c", "#377eb8", "#4daf4a", "#984ea3"]

fig, axs = plt.subplots(2, 2, figsize=(7, 7))
plot_slice(center, center_color, ax=axs[0, 0])
plot_slice(new_slices[0], slice_colors[0], ax=axs[0, 0])

plot_slice(center, center_color, ax=axs[0, 1])
plot_slice(new_slices[1], slice_colors[1], ax=axs[0, 1])

plot_slice(center, center_color, ax=axs[1, 0])
plot_slice(new_slices[2], slice_colors[2], ax=axs[1, 0])

plot_slice(center, center_color, ax=axs[1, 1])
plot_slice(new_slices[3], slice_colors[3], ax=axs[1, 1])
plt.show()

../_images/notebooks_paste_tutorial_48_0.png

Gpu Implementation

POT allows us to write backend agnostic code, allowing us to use Numpy, Pytorch, etc to calculate our computations (https://pythonot.github.io/gen_modules/ot.backend.html).

We have updated our code to include gpu support for Pytorch.

First, you want to make sure you have torch installed. One way to check is by running:

[25]:

import ot

ot.backend.get_backend_list()

[25]:

[<ot.backend.NumpyBackend at 0x7fc814f485c0>,
 <ot.backend.TorchBackend at 0x7fc82098b440>]

By default, you should have ot.backend.NumpyBackend(). To use our gpu, make sure you have ot.backend.TorchBackend().

If not, install torch: https://pytorch.org/

Note: From our tests, ot.backend.TorchBackend() is still faster than ot.backend.NumpyBackend() even if you ONLY use cpu, so we recommend trying it if you would like to speed up your calculations.

Now, assuming you have torch installed, we check to make sure you have access to gpu. PASTE automatically does this check for you, but it is still helpful to know if you want to debug why you can’t seem to access your gpu.

[26]:

import torch

torch.cuda.is_available()

[26]:

False

Running PASTE with gpu

Note: Since the breast dataset is small, cpu may actually be faster than gpu in this particular case. For larger datasets, you will see a greater improvement in gpu vs cpu.

First, we read in our data.

[27]:

data_dir = "../../../tests/data/input/"


# Assume that the coordinates of slices are named slice_name + "_coor.csv"
def load_slices(data_dir, slice_names=["slice1", "slice2", "slice3", "slice4"]):
    slices = []
    for slice_name in slice_names:
        slice_i = sc.read_csv(data_dir + slice_name + ".csv")
        slice_i_coor = np.genfromtxt(data_dir + slice_name + "_coor.csv", delimiter=",")
        slice_i.obsm["spatial"] = slice_i_coor
        # Preprocess slices
        sc.pp.filter_genes(slice_i, min_counts=15)
        sc.pp.filter_cells(slice_i, min_counts=100)
        slices.append(slice_i)
    return slices


slices = load_slices(data_dir)
slice1, slice2, slice3, slice4 = slices

Next, running with gpu is as easy as setting two parameters in our function.

[28]:

start = time.time()

pi12 = pairwise_align(slice1, slice2, backend=ot.backend.TorchBackend(), use_gpu=True)
pi23 = pairwise_align(slice2, slice3, backend=ot.backend.TorchBackend(), use_gpu=True)
pi34 = pairwise_align(slice3, slice4, backend=ot.backend.TorchBackend(), use_gpu=True)

print("Runtime: " + str(time.time() - start))

(INFO) (paste.py) (24-Oct-24 15:05:53) GPU is not available, resorting to torch CPU.
(INFO) (paste.py) (24-Oct-24 15:05:53) GPU is not available, resorting to torch CPU.
(INFO) (paste.py) (24-Oct-24 15:05:54) GPU is not available, resorting to torch CPU.
Runtime: 0.36854100227355957

[29]:

pd.DataFrame(pi12.cpu().numpy())

[29]:

	0	1	2	3	4	5	6	7	8	9	...	240	241	242	243	244	245	246	247	248	249
0	0.003937	0.000000	0.000000	0.0	0.0	0.000000	0.000000	0.0	0.0	0.0	...	0.0	0.000000	0.000000	0.000000	0.0	0.0	0.0	0.000000e+00	0.000000	0.000000
1	0.000063	0.003874	0.000000	0.0	0.0	0.000000	0.000000	0.0	0.0	0.0	...	0.0	0.000000	0.000000	0.000000	0.0	0.0	0.0	0.000000e+00	0.000000	0.000000
2	0.000000	0.000000	0.000000	0.0	0.0	0.003937	0.000000	0.0	0.0	0.0	...	0.0	0.000000	0.000000	0.000000	0.0	0.0	0.0	0.000000e+00	0.000000	0.000000
3	0.000000	0.000126	0.003811	0.0	0.0	0.000000	0.000000	0.0	0.0	0.0	...	0.0	0.000000	0.000000	0.000000	0.0	0.0	0.0	0.000000e+00	0.000000	0.000000
4	0.000000	0.000000	0.000000	0.0	0.0	0.000000	0.003874	0.0	0.0	0.0	...	0.0	0.000000	0.000000	0.000000	0.0	0.0	0.0	0.000000e+00	0.000000	0.000000
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
249	0.000000	0.000000	0.000000	0.0	0.0	0.000000	0.000000	0.0	0.0	0.0	...	0.0	0.000000	0.000000	0.000000	0.0	0.0	0.0	3.937008e-03	0.000000	0.000000
250	0.000000	0.000000	0.000000	0.0	0.0	0.000000	0.000000	0.0	0.0	0.0	...	0.0	0.000000	0.000000	0.000000	0.0	0.0	0.0	6.299213e-05	0.003874	0.000000
251	0.000000	0.000000	0.000000	0.0	0.0	0.000000	0.000000	0.0	0.0	0.0	...	0.0	0.000000	0.000126	0.003811	0.0	0.0	0.0	3.035766e-17	0.000000	0.000000
252	0.000000	0.000000	0.000000	0.0	0.0	0.000000	0.000000	0.0	0.0	0.0	...	0.0	0.003748	0.000000	0.000189	0.0	0.0	0.0	0.000000e+00	0.000000	0.000000
253	0.000000	0.000000	0.000000	0.0	0.0	0.000000	0.000000	0.0	0.0	0.0	...	0.0	0.000000	0.000000	0.000000	0.0	0.0	0.0	0.000000e+00	0.000000	0.003937